About Jean-Yves Girard

Solution 1:

As suggested by @rschwieb, I sent an email to Girard. Here is his answer:

Hi,

The general idea is that logic should not have an adjective: look at modal, non-monotonic, paraconsistent logics in which the adjective is a sort of negation, like in « military justice ».

Linear logic is just a way to do plain logic, i.e. to study pure reasoning. My position was that linearity is a question of fine structure: even if you are concerned with intuitionism, the use of linearimplication can be very helpful.

More recently I discovered that predicate calculus is based on a mistake, namely the idea of « a property of individuals » P(t): we cannot speak of « blue » but only say « the sky is blue ». This realistic contraption makes equality a nonsense. It is indeed possible to expel the « individuals » and replace them, when needed, with linear propositions T, U, V, in which case equality becomes linear equivalence. For this we absolutely need linearity since we can prove (classically or intuitionistically) that there are no more than two « individuals ».

To sum up, I am not a linear logician because the natural treatment of logic compels us into using linearity, this independently of any commitment.

Best regards,

J-YG

Solution 2:

To put this in context, one of Girard's several claims to fame is being the inventor of linear logic, a specialized kind of logic with applications in theoretical computer science and several other places.

If he denies being a "linear logician", it could either be understood as a way to distance himself from that particular system (it's old hat to him, he has long since moved on), or as a way to stress that linear logic is not all he does, or even as a way to say that there's no such thing as a "linear logician" at all (i.e. that linear logic is not a philosophical position one can take instead of ordinary logic, but merely an interesting game one can choose to play when it makes sense).

Or perhaps he meant something completely different. He is often not an easy person to understand and seems to have a fondness for provocative phrasings that the listener is left to make sense of for himself. I once had the experience of sitting through a series of several very animated lectures by him at a summer school, and only getting the faintest idea what he was doing, or what he was trying to achieve. Later on, I followed some other lectures by one of his colleagues who tried to explain his work more accessibly, but who admitted up front that he was not entirely sure he understood it correctly ...

Since the quote is attributed to a particular time and place (apparently a meeting/workshop about linear logic specifically), it looks likely to me that it must have been an off-the-cuff spoken remark by Girard during the meeting, perhaps seizing the opportunity to crack a joke at the expense of someone saying, for example, "we're all linear logicians here". If something like that is the case, looking for a deeper meaning in the statement is almost certainly futile.

Unless the book where you found the quote uses it to illustrate an explicit point, I would guess it's just there because the author found it funny.